Poorly designed websites can create unnecessary barriers for people with disabilities, just as poorly designed buildings prevent some people with disabilities from entering. Access problems often occur because website designers mistakenly assume that everyone sees and accesses a webpage in the same way. This mistaken assumption can frustrate assistive technologies and their users. Accessible website design recognizes these differences and does not require people to see, hear, or use a standard mouse in order to access the information and services provided.
Case law has been the most helpful in illuminating the implications of the ADA for websites.There have been lawsuits involving companies like Expedia, Hotels.com, Southwest Airlines, and Target as defendants and primarily featuring accessibility organizations as plaintiffs. These cases had mixed results, but each helped clarify the ADA's jurisdiction on the web. 
Hey OB – Disclaimer – none of this is legal advice and you’d want to check with a lawyer to know if you’re at risk for any action if you’re not ADA compliant. Based on what we’ve seen if you don’t have a physical retail or service location, and you don’t receive any funding from the government you likely aren’t required to have a website that would be considered compliant. Some people expect that to change in the next few years, but that’s what we know for now. Let us know if you have more questions or would like to test your site.
Ensuring your website is ADA compliant takes skill and know-how. Even with drag-and-drop and state-of-the-art web builders, knowing how to put together content, add alt-tags and compliant contrasting colors just to name a few thing, it takes someone familiar with coding, UI/UX techniques and the best practices advised by the W3C (World Wide Web Consortium) to ensure that your site meets at minimum the A Level of Conformance. Here is the W3C’s complete and exhaustive list of technical conformance guidelines.

The legal issue for websites is whether website operators are operating “a place of public accommodation.” The statute lists 12 different types of public accommodations including somewhat of a catchall that includes “other sales or rental establishment.” The list, created when the law was passed in 1988, conceivably covers most commercial establishments, but does not expressly include websites.

WCAG guidelines break accessibility issues down into three levels. Level A issues are the most urgent and include problems that can severely limit a disabled visitor’s ability to navigate or use the website. Level AA issues tend to be more rooted in functionality, addressing areas where improvement is needed to give disabled users the full experience of a site. (Level AA is considered the target standard for most commercial websites.) Level AAA issues are the highest standard, fine-tuning and expanding on issues identified as Level A and AA. While it is an excellent goal, full Level AAA compliance is likely beyond the reach of most websites.
Most recently, however, pizza chain Domino's has been brought under suit for their website not being accessible for specialty ordering. The U.S. Supreme Court refused to review the case, instead upholding the decision of the 9th U.S. Circuit Court of Appeals who said the “alleged inaccessibility of Domino’s website and app impedes access to the goods and services of its physical pizza franchises—which are places of public accommodation.”